Project ForgeConsider one-dimensional steady state heat conduction along x-axis (0≤x≤L), through a plane wall with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.
- AThe direction of heat transfer will be from the surface at 100°C to the surface at 0°C.
- The maximum temperature inside the wall must be greater than 100°C.
- CThe temperature distribution is linear within the wall.
- DThe temperature distribution is symmetric about the mid-plane of the wall.
Explanation
By superposition, T(x) = T_linear(x) + T_generation(x), where T_linear is the straight-line profile that would exist with these boundary temperatures and NO generation, and T_generation(x) = (qgen/2k)·x(L−x) is the extra 'bulge' caused purely by the uniform generation, satisfying zero at both boundaries and strictly positive everywhere in between. So the actual profile lies everywhere above the no-generation straight line — ruling out (C) linear and (D) symmetric (the boundary values themselves are unequal). This generation-driven elevation is what can push the interior maximum above the higher boundary value of 100°C — the standard justification for option (B). (A) isn't guaranteed either, since heat generation can locally reverse the flow direction near a boundary.
Source: GATE ME 2013 (Booklet Code A) (2013)
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